Introduction to R language
Dae-Jin Lee < dlee@bcamath.org >
BCAM-UPV/EHU Courses 2018-2019
Install and load an R library
Install a package
install.packages("DAAG") # (Data Analysis And Graphics)
or several packages
install.packages(c("lattice","HSAUR2","Hmisc","psych","foreign","xlsx","maps","maptools","RColorBrewer","calibrate"))
In Rstudio (go to Packages and click Install)
Once installed the package, load it
library(DAAG) # or require(DAAG)
Start with R
- Get current working directory
- list the objects in the current workspace
- work with your previous commands
history() # display last 25 commands
history(max.show=Inf) # display all previous commands
- save your command history
savehistory(file="myfile") # default is ".Rhistory"
- recall your command history
loadhistory(file="myfile") # default is ".Rhistory"
- save the workspace to the file
.RData
- save specific objects to a file if you don't specify the path, the cwd is assumed
save(<object list>,file="myfile.RData")
- load a workspace into the current session
- quit
R. You will be prompted to save the workspace.
Reading data in R
The R console
x <- c(7.82,8.00,7.95) # c means "combine"
x
## [1] 7.82 8.00 7.95
A quicker way is to use scan()
x <- scan() # enter a number followed by return and blank line to end
1: 7.82
2: 8.00
3: 7.95
4:
Read 3 items
To create a character vector use ""
id <- c("John","Paul","George","Ringo")
To read a character vector
id <- scan(,"")
1: John
2: Paul
3: George
4: Ringo
5:
Read 4 items
## [1] "John" "Paul" "George" "Ringo"
Data Import
In most situations, we need to read data from a separate data file. There are several methods for doing this.
scan() (see ?scan for help)
cat("Example:", "2 3 5 7", "11 13 17", file = "ex.txt", sep = "\n") # creates ex.txt
scan("ex.txt", skip = 1)
## [1] 2 3 5 7 11 13 17
scan("ex.txt", skip = 1, nlines = 1) # only 1 line after the skipped one
## [1] 2 3 5 7
unlink("ex.data") # tidy up
Several formats are available (.txt, .csv, .xls, .xlsx, SAS, Stata, etc...)
Some R libraries to import data are
library(gdata)
library(foreign)
- Read data from a
.txt or .csv files
Create a folder, name it data and download cars data (cardata.zip)
mydata1 = read.table("data/cardata.txt")
mydata2 = read.csv("data/cardata.csv")
- Other formats
.xls and .xlsx
library(gdata)
mydata3 = read.xls("data/cardata.xls", sheet = 1, header = TRUE)
library(xlsx)
mydata4 = read.xlsx("data/cardata.xlsx", sheetIndex = 1, header = TRUE,colClasses=NA)
- Minitab, SPSS, SAS or Stata
library(foreign)
mydata = read.mtp("mydata.mtp") # Minitab
mydata = read.spss("myfile", to.data.frame=TRUE) # SPSS
mydata = read.dta("mydata.dta") # Stata
library(Hmisc)
mydata = spss.get("mydata.por", use.value.labels=TRUE) # SPSS
Exporting data
mtcars
?mtcars
write.table(mtcars, "cardata.txt", sep="\t")
library(xlsx)
write.xlsx(mydata, "mydata.xlsx")
Data vectors
weight<-c(60,72,57,90,95,72)
class(weight)
## [1] "numeric"
height<-c(1.75,1.80,1.65,1.90,1.74,1.91)
- calculate Body Mass Index
bmi<- weight/height^2
bmi
## [1] 19.59184 22.22222 20.93664 24.93075 31.37799 19.73630
Basic statistics
- mean, median, st dev, variance
mean(weight)
median(weight)
sd(weight)
var(weight)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 57.00 63.00 72.00 74.33 85.50 95.00
min(weight)
max(weight)
range(weight)
sum(weight)
length(weight)
There are several quartiles of an observation variable. The first quartile, or lower quartile, is the value that cuts off the first 25% of the data when it is sorted in ascending order. The second quartile, or median, is the value that cuts off the first 50%. The third quartile, or upper quartile, is the value that cuts off the first 75%.
## 0% 25% 50% 75% 100%
## 57.0 63.0 72.0 85.5 95.0
The \(n^{\rm th}\) percentile of an observation variable is the value that cuts off the first \(n\) percent of the data values when it is sorted in ascending order.
quantile(weight,c(0.32,0.57,0.98))
## 32% 57% 98%
## 67.2 72.0 94.5
- Covariance and correlation
The covariance of two variables \(x\) and \(y\) in a data sample measures how the two are linearly related. A positive covariance would indicate a positive linear relationship between the variables, and a negative covariance would indicate the opposite.
\[
\rm{Cov}(x,y) = \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})
\]
## [1] 0.6773333
The correlation coefficient of two variables in a data sample is their covariance divided by the product of their standard deviations. It is a normalised measurement of how the two are linearly related.
Formally, the sample correlation coefficient is defined by the following formula, where \(\sigma_x\) and \(\sigma_y\) are the sample standard deviations, and \(\sigma_xy\) is the covariance.
\[
\rho_{xy} = \frac{\sigma_{xy}}{\sigma_x~\sigma_y}
\]
## [1] 0.437934
Creating your own functions in R
One of the great strengths of R is the user's ability to add functions. In fact, many of the functions in R are actually functions of functions. The structure of a function is given below.
myfunction <- function(arg1, arg2, ... ){
statements
return(object)
}
f <- function(x){
x^2
}
f
## function(x){
## x^2
## }
Example:
## [1] 4
# Given a vector
x <- c(1,2,-4,7)
f(x)
## [1] 1 4 16 49
Let us create a function that returns a set of summary statistics given a numeric vector:
mysummary <- function(x){
mean <- sum(x)/length(x)
var <- var(x)
sd <- sd(x)
range <- range(x)
result <- list(mean=mean,var=var,sd=sd,range=range)
return(result)
}
Then
set.seed(1234)
x <- rnorm(10)
stats <- mysummary(x)
stats
## $mean
## [1] -0.3831574
##
## $var
## [1] 0.9915928
##
## $sd
## [1] 0.9957875
##
## $range
## [1] -2.345698 1.084441
Character vectors and factor variables
subject <- c("John","Peter","Chris","Tony","Mary","Jane")
sex <- c("MALE","MALE","MALE","MALE","FEMALE","FEMALE")
class(subject)
## [1] "character"
## sex
## FEMALE MALE
## 2 4
Data frames
A data.frame is a table or a two-dimensional array-like structure in which each column contains values of one variable and each row contains one set of values from each column.
Dat <- data.frame(subject,sex,weight,height)
# add bmi to Dat
Dat$bmi <- bmi # or Dat$bmi <- weight/height^2
class(Dat)
## [1] "data.frame"
str(Dat) # display object structure
## 'data.frame': 6 obs. of 5 variables:
## $ subject: Factor w/ 6 levels "Chris","Jane",..: 3 5 1 6 4 2
## $ sex : Factor w/ 2 levels "FEMALE","MALE": 2 2 2 2 1 1
## $ weight : num 60 72 57 90 95 72
## $ height : num 1.75 1.8 1.65 1.9 1.74 1.91
## $ bmi : num 19.6 22.2 20.9 24.9 31.4 ...
# Change rownames
rownames(Dat)<-c("A","B","C","D","E","F")
# Access to data frame elements (similar to a matrix)
Dat[,1] # 1st column
## [1] John Peter Chris Tony Mary Jane
## Levels: Chris Jane John Mary Peter Tony
Dat[,1:3] # 1st to 3rd columns
## subject sex weight
## A John MALE 60
## B Peter MALE 72
## C Chris MALE 57
## D Tony MALE 90
## E Mary FEMALE 95
## F Jane FEMALE 72
Dat[1:2,] # 1st to 2nd row
## subject sex weight height bmi
## A John MALE 60 1.75 19.59184
## B Peter MALE 72 1.80 22.22222
Working with data frames
Example: Analyze data by groups
- Obtain the mean weight, height and BMI means by FEMALES and MALES:
- Select each group and compute the mean
Dat[sex=="MALE",]
Dat[sex=="FEMALE",]
mean(Dat[sex=="MALE",3]) # weight average of MALEs
mean(Dat[sex=="MALE","weight"])
- Use
apply by columns
apply(Dat[sex=="FEMALE",3:5],2,mean)
apply(Dat[sex=="MALE",3:5],2,mean)
# we can use apply with our own function
apply(Dat[sex=="FEMALE",3:5],2,function(x){x+2})
by and colMeans
# 'by' splits your data by factors and do calculations on each subset.
by(Dat[,3:5],sex, colMeans)
aggregate
# another option
aggregate(Dat[,3:5], by=list(sex),mean)
Logical vectors
- Choose individuals with
BMI>22
bmi
bmi>22
as.numeric(bmi>22) # convert a logical condition to a numeric value 0/1
which(bmi>22) # gives the position of bmi for which bmi>22
- Which are between \(20\) and \(25\)?
bmi > 20 & bmi < 25
which(bmi > 20 & bmi < 25)
Working with vectors
x <- c(2, 3, 5, 2, 7, 1)
y <- c(10, 15, 12)
z <- c(x,y) # concatenates x and y
zz <- list(x,y) # create a list
unlist(zz) # unlist the list converting it to a concatenated vector
## [1] 2 3 5 2 7 1 10 15 12
## [1] 2 5 2
x[-c(2,6)] # negative subscripts omit the chosen elements
## [1] 2 5 2 7
## [1] 1 2 3 4 5 6 7 8 9
## [1] 1 2 3 4 5 6 7 8 9
## [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0
## [1] 1.000000 1.421053 1.842105 2.263158 2.684211 3.105263 3.526316
## [8] 3.947368 4.368421 4.789474 5.210526 5.631579 6.052632 6.473684
## [15] 6.894737 7.315789 7.736842 8.157895 8.578947 9.000000
oops <- c(7,9,13)
rep(oops,3) # repeats the entire vector "oops" three times
rep(oops,1:3) # this function has the number 3 replaced
# by a vector with the three values (1,2,3)
# indicating that 7 should be repeated once, 9 twice and 13 three times.
rep(c(2,3,5), 4)
rep(1:2,c(10,15))
rep(c("MALE","FEMALE"),c(4,2)) # it also works with character vectors
c(rep("MALE",3), rep("FEMALE",2))
Matrices and arrays
## [1] 1 2 3 4 5 6 7 8 9 10 11 12
dim(x)<-c(3,4) # 3 rows and 4 columns
X <- matrix(1:12,nrow=3,byrow=TRUE)
X
## [,1] [,2] [,3] [,4]
## [1,] 1 2 3 4
## [2,] 5 6 7 8
## [3,] 9 10 11 12
X <- matrix(1:12,nrow=3,byrow=FALSE)
X
## [,1] [,2] [,3] [,4]
## [1,] 1 4 7 10
## [2,] 2 5 8 11
## [3,] 3 6 9 12
# rownames, colnames
rownames(X) <- c("A","B","C")
X
## [,1] [,2] [,3] [,4]
## A 1 4 7 10
## B 2 5 8 11
## C 3 6 9 12
colnames(X) <- LETTERS[4:7]
X
## D E F G
## A 1 4 7 10
## B 2 5 8 11
## C 3 6 9 12
colnames(X) <- month.abb[4:7]
X
## Apr May Jun Jul
## A 1 4 7 10
## B 2 5 8 11
## C 3 6 9 12
- Column/Row bind operations
cbind(), rbind()
Y <- matrix(0.1*(1:12),3,4)
cbind(X,Y) # bind column-wise
## Apr May Jun Jul
## A 1 4 7 10 0.1 0.4 0.7 1.0
## B 2 5 8 11 0.2 0.5 0.8 1.1
## C 3 6 9 12 0.3 0.6 0.9 1.2
rbind(X,Y) # bind row-wise
## Apr May Jun Jul
## A 1.0 4.0 7.0 10.0
## B 2.0 5.0 8.0 11.0
## C 3.0 6.0 9.0 12.0
## 0.1 0.4 0.7 1.0
## 0.2 0.5 0.8 1.1
## 0.3 0.6 0.9 1.2
Factors
`Factors are the data objects which are used to categorize the data and store it as levels.
gender<-c(rep("female",691),rep("male",692))
is.factor(gender)
## [1] FALSE
## [1] "character"
# change vector to factor (i.e. a category)
gender<- factor(gender)
is.factor(gender)
## [1] TRUE
## [1] "female" "male"
## female male
## 691 692
## gender
## female male
## 691 692
status<- c(0,3,2,1,4,5) # This command creates a numerical vector pain,
# encoding the pain level of five patients.
fstatus <- factor(status, levels=0:5)
levels(fstatus) <- c("student","engineer","unemployed","lawyer","economist","dentist")
Dat$status <- fstatus
Dat
## subject sex weight height bmi status
## A John MALE 60 1.75 19.59184 student
## B Peter MALE 72 1.80 22.22222 lawyer
## C Chris MALE 57 1.65 20.93664 unemployed
## D Tony MALE 90 1.90 24.93075 engineer
## E Mary FEMALE 95 1.74 31.37799 economist
## F Jane FEMALE 72 1.91 19.73630 dentist
- Changing the order of Levels:
data <- c("East","West","East","North","North","East","West",
"West","West","East","North")
# Create the factors
factor_data <- factor(data)
print(factor_data)
## [1] East West East North North East West West West East North
## Levels: East North West
# Apply the factor function with required order of the level.
new_order_data <- factor(factor_data,levels = c("East","West","North"))
print(new_order_data)
## [1] East West East North North East West West West East North
## Levels: East West North
Indexing vector with logicals
a <- c(1,2,3,4,5)
b <- c(TRUE,FALSE,FALSE,TRUE,FALSE)
max(a[b])
## [1] 4
## [1] 5
Missing values
In R, missing values are represented by the symbol NA (not available) . Impossible values (e.g., dividing by zero) are represented by the symbol NaN (not a number).
a <- c(1,2,3,4,NA)
sum(a)
## [1] NA
Excluding missing values from functions
## [1] 10
a <- c(1,2,3,4,NA)
is.na(a)
## [1] FALSE FALSE FALSE FALSE TRUE
The function complete.cases() returns a logical vector indicating which cases are complete.
## [1] TRUE TRUE TRUE TRUE FALSE
The function na.omit() returns the object with listwise deletion of missing values.
## [1] 1 2 3 4
## attr(,"na.action")
## [1] 5
## attr(,"class")
## [1] "omit"
NA in data frames:
require(graphics)
?airquality
str(airquality)
## 'data.frame': 153 obs. of 6 variables:
## $ Ozone : int 41 36 12 18 NA 28 23 19 8 NA ...
## $ Solar.R: int 190 118 149 313 NA NA 299 99 19 194 ...
## $ Wind : num 7.4 8 12.6 11.5 14.3 14.9 8.6 13.8 20.1 8.6 ...
## $ Temp : int 67 72 74 62 56 66 65 59 61 69 ...
## $ Month : int 5 5 5 5 5 5 5 5 5 5 ...
## $ Day : int 1 2 3 4 5 6 7 8 9 10 ...
pairs(airquality, panel = panel.smooth, main = "airquality data")
ok <- complete.cases(airquality)
airquality[ok,]
## Ozone Solar.R Wind Temp Month Day
## 1 41 190 7.4 67 5 1
## 2 36 118 8.0 72 5 2
## 3 12 149 12.6 74 5 3
## 4 18 313 11.5 62 5 4
## 7 23 299 8.6 65 5 7
## 8 19 99 13.8 59 5 8
## 9 8 19 20.1 61 5 9
## 12 16 256 9.7 69 5 12
## 13 11 290 9.2 66 5 13
## 14 14 274 10.9 68 5 14
## 15 18 65 13.2 58 5 15
## 16 14 334 11.5 64 5 16
## 17 34 307 12.0 66 5 17
## 18 6 78 18.4 57 5 18
## 19 30 322 11.5 68 5 19
## 20 11 44 9.7 62 5 20
## 21 1 8 9.7 59 5 21
## 22 11 320 16.6 73 5 22
## 23 4 25 9.7 61 5 23
## 24 32 92 12.0 61 5 24
## 28 23 13 12.0 67 5 28
## 29 45 252 14.9 81 5 29
## 30 115 223 5.7 79 5 30
## 31 37 279 7.4 76 5 31
## 38 29 127 9.7 82 6 7
## 40 71 291 13.8 90 6 9
## 41 39 323 11.5 87 6 10
## 44 23 148 8.0 82 6 13
## 47 21 191 14.9 77 6 16
## 48 37 284 20.7 72 6 17
## 49 20 37 9.2 65 6 18
## 50 12 120 11.5 73 6 19
## 51 13 137 10.3 76 6 20
## 62 135 269 4.1 84 7 1
## 63 49 248 9.2 85 7 2
## 64 32 236 9.2 81 7 3
## 66 64 175 4.6 83 7 5
## 67 40 314 10.9 83 7 6
## 68 77 276 5.1 88 7 7
## 69 97 267 6.3 92 7 8
## 70 97 272 5.7 92 7 9
## 71 85 175 7.4 89 7 10
## 73 10 264 14.3 73 7 12
## 74 27 175 14.9 81 7 13
## 76 7 48 14.3 80 7 15
## 77 48 260 6.9 81 7 16
## 78 35 274 10.3 82 7 17
## 79 61 285 6.3 84 7 18
## 80 79 187 5.1 87 7 19
## 81 63 220 11.5 85 7 20
## 82 16 7 6.9 74 7 21
## 85 80 294 8.6 86 7 24
## 86 108 223 8.0 85 7 25
## 87 20 81 8.6 82 7 26
## 88 52 82 12.0 86 7 27
## 89 82 213 7.4 88 7 28
## 90 50 275 7.4 86 7 29
## 91 64 253 7.4 83 7 30
## 92 59 254 9.2 81 7 31
## 93 39 83 6.9 81 8 1
## 94 9 24 13.8 81 8 2
## 95 16 77 7.4 82 8 3
## 99 122 255 4.0 89 8 7
## 100 89 229 10.3 90 8 8
## 101 110 207 8.0 90 8 9
## 104 44 192 11.5 86 8 12
## 105 28 273 11.5 82 8 13
## 106 65 157 9.7 80 8 14
## 108 22 71 10.3 77 8 16
## 109 59 51 6.3 79 8 17
## 110 23 115 7.4 76 8 18
## 111 31 244 10.9 78 8 19
## 112 44 190 10.3 78 8 20
## 113 21 259 15.5 77 8 21
## 114 9 36 14.3 72 8 22
## 116 45 212 9.7 79 8 24
## 117 168 238 3.4 81 8 25
## 118 73 215 8.0 86 8 26
## 120 76 203 9.7 97 8 28
## 121 118 225 2.3 94 8 29
## 122 84 237 6.3 96 8 30
## 123 85 188 6.3 94 8 31
## 124 96 167 6.9 91 9 1
## 125 78 197 5.1 92 9 2
## 126 73 183 2.8 93 9 3
## 127 91 189 4.6 93 9 4
## 128 47 95 7.4 87 9 5
## 129 32 92 15.5 84 9 6
## 130 20 252 10.9 80 9 7
## 131 23 220 10.3 78 9 8
## 132 21 230 10.9 75 9 9
## 133 24 259 9.7 73 9 10
## 134 44 236 14.9 81 9 11
## 135 21 259 15.5 76 9 12
## 136 28 238 6.3 77 9 13
## 137 9 24 10.9 71 9 14
## 138 13 112 11.5 71 9 15
## 139 46 237 6.9 78 9 16
## 140 18 224 13.8 67 9 17
## 141 13 27 10.3 76 9 18
## 142 24 238 10.3 68 9 19
## 143 16 201 8.0 82 9 20
## 144 13 238 12.6 64 9 21
## 145 23 14 9.2 71 9 22
## 146 36 139 10.3 81 9 23
## 147 7 49 10.3 69 9 24
## 148 14 20 16.6 63 9 25
## 149 30 193 6.9 70 9 26
## 151 14 191 14.3 75 9 28
## 152 18 131 8.0 76 9 29
## 153 20 223 11.5 68 9 30
Working with data frames
- A data frame is used for storing data tables. It is a list of vectors of equal length.
mtcars
?mtcars # or help(mtcars)
## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1
- Structure of the data frame
str(mtcars) # display the structure of the data frame
## 'data.frame': 32 obs. of 11 variables:
## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ cyl : num 6 6 4 6 8 6 8 4 4 6 ...
## $ disp: num 160 160 108 258 360 ...
## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...
## $ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...
## $ qsec: num 16.5 17 18.6 19.4 17 ...
## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...
## $ am : num 1 1 1 0 0 0 0 0 0 0 ...
## $ gear: num 4 4 4 3 3 3 3 4 4 4 ...
## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...
mtcars["Mazda RX4",] # using rows and columns names
mtcars[c("Datsun 710", "Camaro Z28"),]
There are some packages that include particular functions to summarize data frames, for instance the library psych has the function describe
library(psych)
describe(mtcars)
Basic plotting and data analysis in R
data("mtcars")
attach(mtcars) #?attach
plot(wt, mpg, main="Scatterplot Example",
xlab="Car Weight", ylab="Miles Per Gallon", pch=19)
pairs(~mpg+disp+drat+wt,data=mtcars,
main="Simple Scatterplot Matrix")
tab <- table(mtcars[,c("cyl")])
barplot(tab)
Exercises:
- The data.frame
VADeaths contains the death rates per 1000 in Virginia (US) in 1940. The death rates are measured per 1000 population per year. They are cross-classified by age group (rows) and population group (columns).
## Rural Male Rural Female Urban Male Urban Female
## 50-54 11.7 8.7 15.4 8.4
## 55-59 18.1 11.7 24.3 13.6
## 60-64 26.9 20.3 37.0 19.3
## 65-69 41.0 30.9 54.6 35.1
## 70-74 66.0 54.3 71.1 50.0
## 50-54 55-59 60-64 65-69 70-74
## 11.050 16.925 25.875 40.400 60.350
## Rural Male Rural Female Urban Male Urban Female
## 32.74 25.18 40.48 25.28
- The
data.frame rainforest contains several variables from different species
library(DAAG)
rainforest
?rainforest
names(rainforest)
##
## Acacia mabellae C. fraseri Acmena smithii B. myrtifolia
## 16 12 26 11
- The
Acmena data.frame is created from rainforest using the function subset.
- Plot the relationship between the wood biomass (
wood) and the diameter of the breast height (dbh). Use also a logarithm scale.
Acmena <- subset(rainforest, species == "Acmena smithii")
- Compute a histogram of variable
dbh using function hist
Create a vector of the positive odd integers less than 100 and remove the values greater than 60 and less than 80.
## [1] 61 63 65 67 69 71 73 75 77 79
Operators
R's binary and logical operators will look very familiar to programmers. Note that binary operators work on vectors and matrices as well as scalars.
Arithmetic Operators
+ |
addition |
- |
subtraction |
* |
multiplication |
/ |
division |
^ or ** |
exponentiation |
x %% y |
modulus (x mod y) 5%%2 is 1 |
x %/% y |
integer division 5%/%2 is 2 |
Logical Operators
< |
less than |
> |
greater than |
<= |
less or equal to |
>= |
greater or equal to |
== |
exactly equal to |
!= |
not equal to |
!x |
Not x |
x|y |
x OR y |
x&y |
x AND y |
isTRUE(x) |
test if x is TRUE |
# An example
x <- c(1:10)
x[(x>8) | (x<5)]
## [1] 1 2 3 4 9 10
# yields 1 2 3 4 9 10
# How it works
x <- c(1:10)
x
## [1] 1 2 3 4 5 6 7 8 9 10
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE
## [1] TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [1] TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE TRUE TRUE
x[c(T,T,T,T,F,F,F,F,T,T)]
## [1] 1 2 3 4 9 10
Control Structures
These allow you to control the flow of execution of a script typically inside of a function. Common ones include:
if, else
for
while
repeat
break
next
return
Conditional Executions
if
if (condition) {
# do something
} else {
# do something else
}
e.g.:
x <- 1:15
if (sample(x, 1) <= 10) { # ?sample
print("x is less than 10")
} else {
print("x is greater than 10")
}
## [1] "x is less than 10"
Vectorization with ifelse
ifelse(x <= 10, "x less than 10", "x greater than 10")
Other valid ways of writing if/else
if (sample(x, 1) < 10) {
y <- 5
} else {
y <- 0
}
y <- if (sample(x, 1) < 10) {
5
} else {
0
}
for
A for loop works on an iterable variable and assigns successive values till the end of a sequence.
for (i in 1:10) {
print(i)
}
## [1] 1
## [1] 2
## [1] 3
## [1] 4
## [1] 5
## [1] 6
## [1] 7
## [1] 8
## [1] 9
## [1] 10
x <- c("apples", "oranges", "bananas", "strawberries")
for (i in x) {
print(x[i])
}
## [1] NA
## [1] NA
## [1] NA
## [1] NA
for (i in 1:4) {
print(x[i])
}
## [1] "apples"
## [1] "oranges"
## [1] "bananas"
## [1] "strawberries"
for (i in seq(x)) {
print(x[i])
}
## [1] "apples"
## [1] "oranges"
## [1] "bananas"
## [1] "strawberries"
for (i in 1:4) print(x[i])
## [1] "apples"
## [1] "oranges"
## [1] "bananas"
## [1] "strawberries"
nested lopps
m <- matrix(1:10, 2)
for (i in seq(nrow(m))) {
for (j in seq(ncol(m))) {
print(m[i, j])
}
}
## [1] 1
## [1] 3
## [1] 5
## [1] 7
## [1] 9
## [1] 2
## [1] 4
## [1] 6
## [1] 8
## [1] 10
while
i <- 1
while (i < 10) {
print(i)
i <- i + 1
}
## [1] 1
## [1] 2
## [1] 3
## [1] 4
## [1] 5
## [1] 6
## [1] 7
## [1] 8
## [1] 9
Be sure there is a way to exit out of a while loop.
Repeat and break
repeat {
# simulations; generate some value have an expectation if within some range,
# then exit the loop
if ((value - expectation) <= threshold) {
break
}
}
Next
for (i in 1:20) {
if (i%%2 == 1) { # %% is the modulus
next
} else {
print(i)
}
}
## [1] 2
## [1] 4
## [1] 6
## [1] 8
## [1] 10
## [1] 12
## [1] 14
## [1] 16
## [1] 18
## [1] 20
Comparison Operators
## [1] TRUE
## [1] FALSE
## [1] TRUE
a <- c(1,2,4,5)
b <- c(1,2,3,5)
a == b
## [1] TRUE TRUE FALSE TRUE
## [1] FALSE FALSE TRUE FALSE
set.seed(1)
a <- rnorm(10)
b <- rnorm(10)
a<b
## [1] TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE TRUE
- greater/less than or equal:
>= <=
set.seed(2)
a <- rnorm(10)
b <- rnorm(10)
a >= b
## [1] FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE TRUE FALSE
## [1] 3 6 9
## [1] "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N" "O" "P" "Q"
## [18] "R" "S" "T" "U" "V" "W" "X" "Y" "Z"
## [1] 18
set.seed(4)
a <- rnorm(10)
a
## [1] 0.2167549 -0.5424926 0.8911446 0.5959806 1.6356180 0.6892754
## [7] -1.2812466 -0.2131445 1.8965399 1.7768632
## [1] 7
## [1] 9
## [1] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1] 2
Logical Operators
z = 1:6
which(2 < z & z > 3)
## [1] 4 5 6
z = 1:6
(z > 2) & (z < 5)
## [1] FALSE FALSE TRUE TRUE FALSE FALSE
## [1] 3 4
x <- c(TRUE,FALSE,0,6)
y <- c(FALSE,TRUE,FALSE,TRUE)
!x
## [1] FALSE TRUE TRUE FALSE
Operators & and | perform element-wise operation producing the result having the length of the longer operand. But && and || examines only the first element of the operands resulting into a single length logical vector. Zero is considered FALSE and non-zero numbers are taken as TRUE.
Example: - && vs &
## [1] FALSE FALSE FALSE TRUE
## [1] FALSE
## [1] TRUE
## [1] TRUE TRUE FALSE TRUE
if statements
if(cond1=true) { cmd1 } else { cmd2 }
if(1==0) {
print(1)
} else {
print(2)
}
## [1] 2
ifelse statement
ifelse(test, true_value, false_value)
x <- 1:10 # Creates sample data
ifelse(x<5 | x>8, x, 0)
## [1] 1 2 3 4 0 0 0 0 9 10
Loops
The most commonly used loop structures in R are for, while and apply loops. Less common are repeat loops. The break function is used to break out of loops, and next halts the processing of the current iteration and advances the looping index.
Writing a simple for loop in R
Suppose you want to do several printouts of the following form: The year is [year] where [year] is equal to 2010, 2011, up to 2015. You can do this as follows:
print(paste("The year is", 2010))
## [1] "The year is 2010"
for
For loops are controlled by a looping vector. In every iteration of the loop one value in the looping vector is assigned to a variable that can be used in the statements of the body of the loop. Usually, the number of loop iterations is defined by the number of values stored in the looping vector and they are processed in the same order as they are stored in the looping vector.
Syntax
for(variable in sequence) {
statements
}
for (j in 1:5)
{
print(j^2)
}
## [1] 1
## [1] 4
## [1] 9
## [1] 16
## [1] 25
Repeat the loop saving the resuls in a vector x.
n = 5
x = NULL # creates a NULL object
for (j in 1:n)
{
x[j] = j^2
}
x
## [1] 1 4 9 16 25
Let's use a for loop to estimate the average of squaring the result of a roll of a dice.
nsides = 6
ntrials = 1000
trials = NULL
for (j in 1:ntrials)
{
trials[j] = sample(1:nsides,1) # We get one sample at a time
}
mean(trials^2)
## [1] 14.563
Example: stop on condition and print error message
x <- 1:10
z <- NULL
for(i in seq(along=x)) {
if (x[i]<5) {
z <- c(z,x[i]-1)
} else {
stop("values need to be <5")
}
}
## Error: values need to be <5
z
## [1] 0 1 2 3
while
Similar to for loop, but the iterations are controlled by a conditional statement.
z <- 0
while(z < 5) {
z <- z + 2
print(z)
}
## [1] 2
## [1] 4
## [1] 6
apply loop family
&nsbp;
For Two-Dimensional Data Sets: apply
Syntax:
apply(X, MARGIN, FUN, ARGs)
X: array, matrix or data.frame; MARGIN: 1 for rows, 2 for columns, c(1,2) for both; FUN: one or more functions; ARGs: possible arguments for function.
## Example for applying predefined mean function
apply(mtcars[,1:3], 1, mean)
## With custom function
x <- 1:10
test <- function(x) { # Defines some custom function
if(x < 5) {
x-1
} else {
x / x
}
}
apply(as.matrix(x), 1, test)
## Same as above but with a single line of code
apply(as.matrix(x), 1, function(x) { if (x<5) { x-1 } else { x/x } })
For Ragged Arrays: tapply
Apply a function to each cell of a ragged array, that is to each (non-empty) group of values given by a unique combination of the levels of certain factors.
## Computes mean values of vector agregates defined by factor
tapply(as.vector(mtcars$mpg), factor(mtcars$cyl), mean)
## 4 6 8
## 26.66364 19.74286 15.10000
## The aggregate function provides related utilities
aggregate(mtcars[,c(1,3,4)], list(mtcars$cyl), mean)
## Group.1 mpg disp hp
## 1 4 26.66364 105.1364 82.63636
## 2 6 19.74286 183.3143 122.28571
## 3 8 15.10000 353.1000 209.21429
For Vectors and Lists: lapply and sapply
Both apply a function to vector or list objects. The function lapply returns a list, while sapply attempts to return the simplest data object, such as vector or matrix instead of list.
Syntax
lapply(X,FUN)
sapply(X,FUN)
## Creates a sample list
mylist <- as.list(mtcars[,c(1,4,6)])
mylist
## $mpg
## [1] 21.0 21.0 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 17.8 16.4 17.3 15.2
## [15] 10.4 10.4 14.7 32.4 30.4 33.9 21.5 15.5 15.2 13.3 19.2 27.3 26.0 30.4
## [29] 15.8 19.7 15.0 21.4
##
## $hp
## [1] 110 110 93 110 175 105 245 62 95 123 123 180 180 180 205 215 230
## [18] 66 52 65 97 150 150 245 175 66 91 113 264 175 335 109
##
## $wt
## [1] 2.620 2.875 2.320 3.215 3.440 3.460 3.570 3.190 3.150 3.440 3.440
## [12] 4.070 3.730 3.780 5.250 5.424 5.345 2.200 1.615 1.835 2.465 3.520
## [23] 3.435 3.840 3.845 1.935 2.140 1.513 3.170 2.770 3.570 2.780
Compute sum of each list component and return result as list
## $mpg
## [1] 642.9
##
## $hp
## [1] 4694
##
## $wt
## [1] 102.952
Compute sum of each list component and return result as vector
## mpg hp wt
## 642.900 4694.000 102.952
Other Loops
Repeat Loop
Syntax
repeat statements
Loop is repeated until a break is specified. This means there needs to be a second statement to test whether or not to break from the loop.
Example:
z <- 0
repeat {
z <- z + 1
print(z)
if(z > 100) break()
}
Looping over very large data sets can become slow in R. However, this limitation can be overcome by eliminating certain operations in loops or avoiding loops over the data intensive dimension in an object altogether. The latter can be achieved by performing mainly vector-to-vector or matrix-to-matrix computations which run often over 100 times faster than the corresponding for() or apply() loops in R. For this purpose, one can make use of the existing speed-optimized R functions (e.g.: rowSums, rowMeans, table, tabulate) or one can design custom functions that avoid expensive R loops by using vector- or matrix-based approaches. Alternatively, one can write programs that will perform all time consuming computations on the C-level.
- Speed comparison of
for loops with an append versus and inject step
N <- 1e3
myMA <- matrix(rnorm(N), N, 10, dimnames=list(1:N, paste("C", 1:10, sep="")))
results <- NULL
system.time(for(i in seq(along=myMA[,1]))
results <- c(results, mean(myMA[i,])))
results <- numeric(length(myMA[,1]))
system.time(for(i in seq(along=myMA[,1]))
results[i] <- mean(myMA[i,]))
The inject approach is 20-50 times faster than the append version.
- Speed comparison of
apply loop versus rowMeans for computing the mean for each row in a large matrix:
system.time(myMAmean <- apply(myMA, 1, mean))
system.time(myMAmean <- rowMeans(myMA))
The rowMeans approach is over 200 times faster than the apply loop.
Scatterplots
library(MASS)
data("mammals")
?mammals
head(mammals)
## body brain
## Arctic fox 3.385 44.5
## Owl monkey 0.480 15.5
## Mountain beaver 1.350 8.1
## Cow 465.000 423.0
## Grey wolf 36.330 119.5
## Goat 27.660 115.0
attach(mammals)
species <- row.names(mammals)
x <- body
y <- brain
library(calibrate)
# scatterplot
plot(x,y, xlab = "body weight in kgr", ylab = "brain weight in gr",
main="Body vs Brain weight \n for 62 Species of Land Mammals",xlim=c(0,8500))
textxy(x,y,labs=species,col = "blue",cex=0.85)
Identify a point in the scatterplot
Plot in the log scale
plot(log(x),log(y), xlab = "log body weight in kgr", ylab = "log brain weight in gr",
main="log Body vs log Brain weight \n for 62 Species of Land Mammals")
textxy(log(x),log(y),labs=species,col = "blue",cex=0.85)
Identify a point in the log scale scatterplot
identify(log(x),log(y),species)
Multiple Data Sets on One Plot
One common task is to plot multiple data sets on the same plot. In many situations, the way to do this is to create the initial plot and then add additional information to the plot. For example, to plot bivariate data the plot command is used to initialise and create the plot. The points command can then be used to add additional datasets to the plot.
set.seed(1234)
x <- rnorm(10,sd=5,mean=20)
y <- 2.5*x - 1.0 + rnorm(10,sd=9,mean=0)
cor(x,y)
## [1] 0.7512194
plot(x,y,xlab="Independent",ylab="Dependent",main="Random plot")
x1 <- runif(8,15,25)
y1 <- 2.5*x1 - 1.0 + runif(8,-6,6)
points(x1,y1,col=2)
with legend and \((x_2,y_2)\) points:
set.seed(1234)
x2 <- runif(8,15,25)
y2 <- 2.5*x2 - 1.0 + runif(8,-6,6)
plot(x,y,xlab="Independent",ylab="Dependent",main="Random plot")
points(x1,y1,col=2,pch=3)
points(x2,y2,col=4,pch=5)
legend("topleft",c("Original","one","two"),col=c(1,2,4),pch=c(1,3,5))
Multiple Graphs on One Image:
set.seed(1234)
par(mfrow=c(2,3))
boxplot(rnorm(100),main="first plot")
boxplot(rgamma(100,2),main="second plot", horizontal=TRUE,col="bisque")
plot(rnorm(100),xlab="third plot",
ylab="y-label",main="x-label")
hist(rnorm(100),main="fourth plot",col="lightgrey")
hist(rexp(100),main="fifth plot",col="blue")
plot(rnorm(100),rexp(100),main="sixth plot")
Pairwise relationships
uData <- rnorm(20)
vData <- rnorm(20,mean=5)
wData <- uData + 2*vData + rnorm(20,sd=0.5)
xData <- -2*uData+rnorm(20,sd=0.1)
yData <- 3*vData+rnorm(20,sd=2.5)
d <- data.frame(u=uData,v=vData,w=wData,x=xData,y=yData)
pairs(d)
Plotting correlations
The function corrplot in the library(corrplot) visualizes a correlation matrix calculate with function cor
## corrplot 0.84 loaded
M <- cor(d)
corrplot(M, method="circle",type="upper")
Plotting surfaces: image, contour and persp plots
x <- seq(0,2*pi,by=pi/50)
y <- x
xg <- (x*0+1) %*% t(y)
yg <- (x) %*% t(y*0+1)
f <- sin(xg*yg)
par(mfrow=c(2,2))
image(x,y,f)
contour(x,y,f)
contour(x,y,f,nlevels=4)
image(x,y,f,col=grey.colors(100))
contour(x,y,f,nlevels=4,add=TRUE,col="red")
Similarly, one can use persp plot
persp(x,y,f,theta=-30,phi=55,col="lightgrey",shade=.01)
Or plot images
library(fields)
data(lennon)
image(lennon,col=grey(seq(0,1,l=256)))
Tables and Cross-classification
library(MASS)
data(quine)
?quine
attach(quine)
table(Sex)
## Sex
## F M
## 80 66
## Age
## Sex F0 F1 F2 F3
## F 10 32 19 19
## M 17 14 21 14
# or xtabs
xtabs(~Sex+Age,data=quine)
## Age
## Sex F0 F1 F2 F3
## F 10 32 19 19
## M 17 14 21 14
xtabs(~Sex+Age+Eth,data=quine)
## , , Eth = A
##
## Age
## Sex F0 F1 F2 F3
## F 5 15 9 9
## M 8 5 11 7
##
## , , Eth = N
##
## Age
## Sex F0 F1 F2 F3
## F 5 17 10 10
## M 9 9 10 7
Calculations of cross-classifications
## F0 F1 F2 F3
## 14.85185 11.15217 21.05000 19.60606
tapply(Days,list(Sex,Age),mean)
## F0 F1 F2 F3
## F 18.70000 12.96875 18.42105 14.00000
## M 12.58824 7.00000 23.42857 27.21429
tapply(Days,list(Sex,Age),function(x) sqrt(var(x)/length(x)))
## F0 F1 F2 F3
## F 4.208589 2.329892 5.299959 2.940939
## M 3.768151 1.418093 3.766122 4.569582
Qualitative data
A data sample is called qualitative, also known as categorical if its values belong to a collection of known defined non-overlapping classes.
Let us consider some artificial data consisting of the treatment and improvement of patients with rheumatoid arthritis.
treatment <- factor(rep(c(1, 2), c(43, 41)), levels = c(1, 2),
labels = c("placebo", "treated"))
improved <- factor(rep(c(1, 2, 3, 1, 2, 3), c(29, 7, 7, 13, 7, 21)),
levels = c(1, 2, 3),
labels = c("none", "some", "marked"))
We can compute a cross-classification table
xtabs(~treatment+improved)
## improved
## treatment none some marked
## placebo 29 7 7
## treated 13 7 21
Graphically,
spineplot(improved ~ treatment)
The R dataset UCBAdmissions contains aggregated data on applicants to graduate school at Berkeley for the six largest departments in 1973 classified by admission and sex.
data("UCBAdmissions")
?UCBAdmissions
apply(UCBAdmissions, c(2,1), sum)
## Admit
## Gender Admitted Rejected
## Male 1198 1493
## Female 557 1278
prop.table(apply(UCBAdmissions, c(2,1), sum))
## Admit
## Gender Admitted Rejected
## Male 0.2646929 0.3298719
## Female 0.1230667 0.2823685
## Dept A B C D E F
## Admit Gender
## Admitted Male 512 353 120 138 53 22
## Female 89 17 202 131 94 24
## Rejected Male 313 207 205 279 138 351
## Female 19 8 391 244 299 317
The same but with a more readable format can be obtained using ftable
ftable(round(prop.table(UCBAdmissions), 3),
row.vars="Dept", col.vars = c("Gender", "Admit"))
## Gender Male Female
## Admit Admitted Rejected Admitted Rejected
## Dept
## A 0.113 0.069 0.020 0.004
## B 0.078 0.046 0.004 0.002
## C 0.027 0.045 0.045 0.086
## D 0.030 0.062 0.029 0.054
## E 0.012 0.030 0.021 0.066
## F 0.005 0.078 0.005 0.070
More interesting are the proportions admitted for each Gender by Dept combination (dimensions 2 and 3 of the array). Notice that male and female admission rates are about the same in all departments, except "A", where female admission rates are higher.
# prop.table(UCBAdmissions, c(2,3))
ftable(round(prop.table(UCBAdmissions, c(2,3)), 2),
row.vars="Dept", col.vars = c("Gender", "Admit"))
## Gender Male Female
## Admit Admitted Rejected Admitted Rejected
## Dept
## A 0.62 0.38 0.82 0.18
## B 0.63 0.37 0.68 0.32
## C 0.37 0.63 0.34 0.66
## D 0.33 0.67 0.35 0.65
## E 0.28 0.72 0.24 0.76
## F 0.06 0.94 0.07 0.93
## Data aggregated over departments
apply(UCBAdmissions, c(1, 2), sum)
## Gender
## Admit Male Female
## Admitted 1198 557
## Rejected 1493 1278
Applications and admissions by department at UC Berkeley can be viewed graphically.
spineplot(margin.table(UCBAdmissions, c(3, 2)),
main = "Applications at UCB")
spineplot(margin.table(UCBAdmissions, c(3, 1)),
main = "Admissions at UCB")
This data set is frequently used for illustrating Simpson's paradox. At issue is whether the data show evidence of sex bias in admission practices. There were 2691 male applicants, of whom 1198 (44.5%) were admitted, compared with 1835 female applicants of whom 557 (30.4%) were admitted. Men were much more successful in admissions than women. Wikipedia: Gender Bias UC Berkeley. See animation at link
Quantitative data
Quantitative data, also known as continuous data, consists of numeric data that support arithmetic operations.
## eruptions waiting
## 1 3.600 79
## 2 1.800 54
## 3 3.333 74
## 4 2.283 62
## 5 4.533 85
## 6 2.883 55
It consists of a collection of observations of the Old Faithful geyser in the USA Yellowstone National Park. Â
There are two observation variables in the dataset. The first one, called eruptions, is the duration of the geyser eruptions. The second one, called waiting, is the length of waiting period until the next eruption. It turns out there is a correlation between the two variables.
Frequency distribution of quantitative data
The frequency distribution of a data variable is a summary of the data occurrence in a collection of non-overlapping categories.
Let us find the frequency distribution of the eruption duration in faithful data set.
duration <- faithful$eruptions
range(duration)
## [1] 1.6 5.1
Â
Now we create the range of non-overlapping sub-intervals by defining a sequence of equal distance break points.
If we round the endpoints of the interval [1.6, 5.1] to the closest half-integers, we come up with the interval [1.5, 5.5]. Hence we set the breakpoints to be the half-integer sequence { 1.5, 2.0, 2.5, ... }.
breaks <- seq(1.5,5.5,by=0.5)
breaks
## [1] 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Â
Classify the eruption durations according to the half-unit-length sub-intervals with cut. As the intervals are to be closed on the left, and open on the right, we set the right argument to FALSE.
duration.cut = cut(duration, breaks, right=FALSE)
Compute the frequency of eruptions in each sub-interval with the table function.
duration.freq = table(duration.cut)
duration.freq
## duration.cut
## [1.5,2) [2,2.5) [2.5,3) [3,3.5) [3.5,4) [4,4.5) [4.5,5) [5,5.5)
## 51 41 5 7 30 73 61 4
hist function does all the computaions to find the frequency distribution:
freq <- hist(duration)
freq
## $breaks
## [1] 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
##
## $counts
## [1] 55 37 5 9 34 75 54 3
##
## $density
## [1] 0.40441176 0.27205882 0.03676471 0.06617647 0.25000000 0.55147059
## [7] 0.39705882 0.02205882
##
## $mids
## [1] 1.75 2.25 2.75 3.25 3.75 4.25 4.75 5.25
##
## $xname
## [1] "duration"
##
## $equidist
## [1] TRUE
##
## attr(,"class")
## [1] "histogram"
freq <- hist(duration,breaks = breaks)
Density estimation builds an estimate of some underlying probability density function using an observed data sample.
library(graphics)
d <- density(faithful$eruptions)
d
##
## Call:
## density.default(x = faithful$eruptions)
##
## Data: faithful$eruptions (272 obs.); Bandwidth 'bw' = 0.3348
##
## x y
## Min. :0.5957 Min. :0.0002262
## 1st Qu.:1.9728 1st Qu.:0.0514171
## Median :3.3500 Median :0.1447010
## Mean :3.3500 Mean :0.1813462
## 3rd Qu.:4.7272 3rd Qu.:0.3086071
## Max. :6.1043 Max. :0.4842095
 Two dimension histogram:
library(gplots)
h2 <- hist2d(faithful, nbins=30,xlab="Duration in minutes",ylab="Waiting")
##
## ----------------------------
## 2-D Histogram Object
## ----------------------------
##
## Call: hist2d(x = faithful, nbins = 30, xlab = "Duration in minutes",
## ylab = "Waiting")
##
## Number of data points: 272
## Number of grid bins: 30 x 30
## X range: ( 1.6 , 5.1 )
## Y range: ( 43 , 96 )
## [1] "counts" "x.breaks" "y.breaks" "x" "y" "nobs"
## [7] "call"
Â
Relative frequencies
duration.relfreq <- duration.freq / nrow(faithful)
tab <- cbind(duration.freq, duration.relfreq)
apply(tab,2,sum)
## duration.freq duration.relfreq
## 272 1
Â
Cumulative frequency distribution
## [1.5,2) [2,2.5) [2.5,3) [3,3.5) [3.5,4) [4,4.5) [4.5,5) [5,5.5)
## 51 92 97 104 134 207 268 272
## [1.5,2) [2,2.5) [2.5,3) [3,3.5) [3.5,4) [4,4.5) [4.5,5)
## 0.1875000 0.3382353 0.3566176 0.3823529 0.4926471 0.7610294 0.9852941
## [5,5.5)
## 1.0000000
Bivariante Density estimation:
data("faithful")
attach(faithful)
Dens2d<-kde2d(eruptions,waiting)
image(Dens2d,xlab="eruptions",ylab="waiting")
contour(Dens2d,add=TRUE,col="black",lwd=2,nlevels=5)
Perspective plot:
persp(Dens2d,phi=30,theta=20,d=5,xlab="eruptions",ylab="waiting",zlab="",shade=.2,col="lightblue",expand=.85,ticktype = "detailed")
Advanced plotting ggplot2
Why ggplot2?
Advantages of ggplot2
consistent underlying `grammar of graphics' (Wilkinson, 2005)
plot specification at a high level of abstraction
very flexible
theme system for polishing plot appearance
mature and complete graphics system
many users, active mailing list
Example: Housing data download
housing <- read.csv("data/landdata-states.csv")
head(housing[1:5])
## State region Date Home.Value Structure.Cost
## 1 AK West 2010.25 224952 160599
## 2 AK West 2010.50 225511 160252
## 3 AK West 2009.75 225820 163791
## 4 AK West 2010.00 224994 161787
## 5 AK West 2008.00 234590 155400
## 6 AK West 2008.25 233714 157458
# change column names
names(housing)[names(housing) == "Land.Share..Pct."] <- "Land.Share.Pct"
head(housing, 10)
## State region Date Home.Value Structure.Cost Land.Value
## 1 AK West 2010.25 224952 160599 64352
## 2 AK West 2010.50 225511 160252 65259
## 3 AK West 2009.75 225820 163791 62029
## 4 AK West 2010.00 224994 161787 63207
## 5 AK West 2008.00 234590 155400 79190
## 6 AK West 2008.25 233714 157458 76256
## 7 AK West 2008.50 232999 160092 72906
## 8 AK West 2008.75 232164 162704 69460
## 9 AK West 2009.00 231039 164739 66299
## 10 AK West 2009.25 229395 165424 63971
## Land.Share.Pct Home.Price.Index Land.Price.Index Year Qrtr
## 1 28.6 1.481 1.552 2010 1
## 2 28.9 1.484 1.576 2010 2
## 3 27.5 1.486 1.494 2009 3
## 4 28.1 1.481 1.524 2009 4
## 5 33.8 1.544 1.885 2007 4
## 6 32.6 1.538 1.817 2008 1
## 7 31.3 1.534 1.740 2008 2
## 8 29.9 1.528 1.660 2008 3
## 9 28.7 1.521 1.587 2008 4
## 10 27.9 1.510 1.536 2009 1
ggplot2 VS Base for simple graphs
Base graphics histogram are:
library(ggplot2)
ggplot(housing, aes(x = Home.Value)) +
geom_histogram()
Another simple graph
plot(Home.Value ~ Date,
data=subset(housing, State == "MA"))
points(Home.Value ~ Date, col="red",
data=subset(housing, State == "TX"))
legend(1975, 400000,
c("MA", "TX"), title="State",
col=c("black", "red"),
pch=c(1, 1))
ggplot version, colored scatter plot example:
ggplot(subset(housing, State %in% c("MA", "TX")),
aes(x=Date,
y=Home.Value,
color=State))+
geom_point()
Geometric Objects And Aesthetics
*Aesthetic Mapping:*
In ggplot land /aesthetic/ means "something you can see". Examples include:
Each type of geom accepts only a subset of all aesthetics--refer to the geom help pages to see what mappings each geom accepts. Aesthetic mappings are set with the aes() function.
Geometric Objects (geom)
Geometric objects are the actual marks we put on a plot.
Examples include:
points (geom_point, for scatter plots, dot plots, etc)
lines (geom_line, for time series, trend lines, etc)
boxplot (geom_boxplot, for, boxplots)
A plot must have at least one geom; there is no upper limit. You can add a geom to a plot using the + operator
More at http://had.co.nz/ggplot2/
Some examples:
library(ggplot2)
?qplot
qplot(displ, hwy, data = mpg, colour = factor(cyl))
qplot(mpg, wt, data = mtcars)
qplot(mpg, wt, data = mtcars, colour = cyl)
qplot(mpg, wt, data = mtcars, size = cyl)
qplot(mpg, wt, data = mtcars, size = cyl, alpha = I(0.7))
qplot(mpg, wt, data = mtcars, facets = vs ~ am)
qplot(displ, hwy, data=mpg, facets = . ~ year) + geom_smooth()
p <- ggplot(mtcars)
p <- p + aes(wt, hp)
p + geom_point(aes(colour = factor(cyl)))
p <- ggplot(mtcars, aes(mpg, wt))
p + geom_point(colour = "darkblue")
Get data from the internet
filepath <- "http://idaejin.github.io/courses/R/2018/data/ggplot2_data.txt"
myData<-read.table(file=url(filepath),header=TRUE,sep="\t")
str(myData)
qplot(data=myData,x=BM,main="Histogram of BodyMass")
qplot(data=myData,x=BM,y=var1,log="xy",color=Tribe)
Maps
Example: Malignant Melanoma in the USA
Fisher and Belle (1993) report mortality rates due to malignant melanoma of the skin for white males during the period 1950-1969, for each state on the US mainland.
data("USmelanoma",package="HSAUR2")
head(USmelanoma)
## mortality latitude longitude ocean
## Alabama 219 33.0 87.0 yes
## Arizona 160 34.5 112.0 no
## Arkansas 170 35.0 92.5 no
## California 182 37.5 119.5 yes
## Colorado 149 39.0 105.5 no
## Connecticut 159 41.8 72.8 yes
A data consists of 48 observations on the following 5 variables.
mortality: number of white males died due to malignant melanoma 1950-1969 per one million inhabitants.
latitude: latitude of the geographic centre of the state.
longitude: longitude of the geographic centre of each state.
ocean: a binary variable indicating contiguity to an ocean at levels no or yes.
Plotting mortality rates
xr <- range(USmelanoma$mortality) * c(0.9, 1.1)
Let us plot mortality rates in
#layout(matrix(1:2, nrow = 2))
boxplot(USmelanoma$mortality, ylim = xr, horizontal = TRUE,xlab = "Mortality")
hist(USmelanoma$mortality, xlim = xr, xlab = "", main = "",axes = FALSE, ylab = "")
axis(1)
Malignant melanoma mortality rates by contiguity to an ocean
plot(mortality ~ ocean, data = USmelanoma,
xlab = "Contiguity to an ocean", ylab = "Mortality")
Histograms can often be misleading for displaying distributions because of their dependence on the number of classes chosen. An alternative is to formally estimate the density function of a variable and then plot the resulting estimate.
The estimated densities of malignant melanoma mortality rates by contiguity to an ocean looks like this:
dyes<- with(USmelanoma, density(mortality[ocean == "yes"]))
dno <- with(USmelanoma, density(mortality[ocean == "no"]))
plot(dyes, lty = 1, xlim = xr, main = "", ylim = c(0, 0.018))
lines(dno, lty = 2)
legend("topright", lty = 1:2, legend = c("Coastal State","Land State"), bty = "n")
Now we might move on to look at how mortality rates are related to the geographic location of a state as represented by the latitude and longitude of the centre of the state.
layout(matrix(1:2, ncol = 2))
plot(mortality ~ -longitude, data = USmelanoma)
plot(mortality ~ latitude, data = USmelanoma)
Mapping mortality rates
The data contains the longitude and latitude of the centroids
plot(-USmelanoma$longitude,USmelanoma$latitude,
asp=1.5,cex=.3,pch=19,col="blue")
library("sp")
library("maps")
library("maptools")
library("RColorBrewer")
map("state")
points(-USmelanoma$longitude,USmelanoma$latitude,asp=1.5,cex=.3,pch=19,col="blue")
#qplot(-USmelanoma$longitude,USmelanoma$latitude,colour=USmelanoma$mortality,asp=1.5)+scale_color_gradient(low="blue", high="red")+geom_point()
#Create a function to generate a continuous color palette
rbPal <- colorRampPalette(c('blue','grey','red'))
#This adds a column of color values
# based on the y values
USmelanoma$Col <- (rbPal(10)[as.numeric(cut(USmelanoma$mortality,breaks = 10))])
map("state",xlim=c(-135,-65))
points(-USmelanoma$longitude,USmelanoma$latitude,col=USmelanoma$Col,asp=1.5,pch=19,cex=1.2)
legend("topleft",title="Decile",legend=quantile(USmelanoma$mortality,
seq(0.1,1,l=10)),col =rbPal(10),pch=15,cex=1.,box.col = NA)
states <- map("state", plot = FALSE, fill = TRUE)
IDs <- sapply(strsplit(states$names, ":"), function(x) x[1])
rownames(USmelanoma) <- tolower(rownames(USmelanoma))
us1 <- map2SpatialPolygons(states, IDs=IDs,proj4string = CRS("+proj=longlat +datum=WGS84"))
us2 <- SpatialPolygonsDataFrame(us1, USmelanoma)
col <- colorRampPalette(c('blue', 'gray80','red'))
spplot(us2, "mortality", col.regions = col(200),
par.settings = list(axis.line = list(col = 'transparent')),
main="Map of the US showing malignant melanoma mortality rates")
Packages for Spatial Regression / Geostatistics / Spatial Point Pattern methods
sp, maptools, spatstatmaps
install.packages(c("sp","maptools","spatstat","maps"))
Basic syntax
map(database = "world",regions=".")
Databases are available for US, France, Italy and New Zealand. For other countries, you need to import a database with the corresponding map.
ggmap offers plotting capabilities like ggplot2
library(ggmap)
geocode("Bilbao, Spain")
## lon lat
## 1 NA NA